The electromagnetic (EM) flowmeter is a fundamental flowmeter. Its basis is a Lorentz transformation: a magnetic induction B in a stationary frame of reference is observed in the moving frame to have the same value of B—but one also observes an electric field E equal to u×B, where u is the velocity of motion. The electric field E, which is the basis of the EM flowmeter, exists solely because of motion. It involves no constitutive parameters: no material properties, such as sound speed, electrical conductivity or permittivity, viscosity, or other. Hence, in principle, it can meter any stuff that can be blown, pumped or extruded through a pipe.
The instrument has no moving parts, is obstructionless, and is non-intrusive. It is linear—thus it correctly meters the average of pulsating flow, and it meters flow in either direction. The present state of the art instrument is limited to conductive fluids. For conductive fluids, a technical discussion of the EM flowmeter can be found in Shercliff, J. A., The Theory Of Electromagnetic Flow Measurement, Cambridge University Press, New York, 1962.
The EM flowmeter was first operated with insulating liquids in the 1960s (see: (1) Cushing, Vincent, Dean Reily and George Edmunds, “Development of an Electromagnetic Flowmeter for Cryogenic Fluids,” Final Report under Contract NASw-381, NASA Lewis Research Center, May 15, 1964; (2) Cushing, Vincent, “Electromagnetic Flowmeter,” Rev Sci Instr, 36, 1142 (1965); (3) (same author as (2)), “Electromagnetic Flowmeter,” FLOW (Proc of May 1971 Flow Symposium) (Roger B Dowdell, ed.) Vol 1, Part 2, ISA, Pitts, (1974), p 723. To ameliorate triboelectric noise, a 1 KHz square wave induction was used. For a literal square wave dφ/dt is theoretically a Dirac pulse; however, eddy currents in the magnet and nearby conductive materials (shielding, housing, . . . ) produce a decaying pulse aftereffect. The signal is sampled as late as possible each half cycle—to allow the aftereffect to decay. But with high frequency induction there is not enough time for the aftereffect to decay adequately; the residual dφ/dt leaves a zero-point offset that has been unacceptable for commercial application.
FIG. 1 shows an established transducer design for the flowmeter (see cited references 1,2,3 plus (4) (same author as (3), “Comprehensive Flowmeter for All Materials,” Final Report under Grant DE-FG05-92ER81353, USDOE Oak Ridge Field Office, Nov. 15, 1999; (5) (same author as (3), “Electromagnetic Flowmeter for All Fluids”, Proc Emerging Technologies Conference 2001, 10–13 Sep. 2001, Houston Tex., ISA Volume 415; (6). (same author as (3), “Electromagnetic Flowmeter for Insulating Liquids,” IEEE Proc Instrumentation and Measurement Technology Conference, 21–23 May 2002, Anchorage Ak.). The metered fluid passes on the interior of a dielectric liner. The sensing and common electrodes are emplaced on the outside surface of the liner. Each electrode is curvilinear, matching the liner's contour; the sensing electrode is of length L. They are wide area electrodes, to provide adequate capacitive coupling (through the liner) to the flow generated voltage. The sensing electrode manifold is guarded on all sides, except through the liner to the metered fluid.
The above-cited references also detail magnet design and magnet drive circuitry; and describe preamplifier circuitry that enables the EM flowmeter to operate optionally as a volumetric flowmeter (for any liquid) or as a mass flowmeter for most insulating liquids.
To minimize high frequency eddy current losses in the several conductive electrode and guard sheets, all sheets are a combination of lower conductivity material superposed with high conductivity stripes, as shown in FIG. 2.
The dielectric liner attenuates (depending on liner thickness) the flow signal. The attenuation factor is computed based on auxiliary, continuous measurement of full-pipe direct capacitance between sensing electrode and common manifolds (see cited reference 3). Initial work was conducted without a liner; but later testing recommended it. Theoretical expressions are simpler without a liner; for simplicity here we omit its consideration.
For a linerless, single-sided (ie, non-balanced) preamplifier input, FIG. 3 shows the EM flowmeter's:
(1) equivalent circuit; and
(2) block diagram of the preamplifier.
The cited references describe:
(1) CG, the direct capacitance between sensing electrode and guard;
(2) C0, the empty-pipe direct capacitance between sensing electrode and common;
(3) R0, the flowmeter's internal resistance; and,
(4) VF, the flow-induced voltage.
The references further provide,C0=2LK0T/π,  (1)VF=vmπaB sin(θ)/T,  (2)where L=length of sensing electrode; K0 is the permittivity of free space (8.85 pF/m); T=loge[sec(θ)+tan(θ)]; 2θ is the angle subtended by the sensing electrode; a is the pipe radius; B is the induction; vm is the mean flow velocity in the circular pipe. R0 and C0 are related by the metered fluid's relaxation time constant τFτF=KFK0/σF=KFC0R0,  (3)where KF is the dielectric constant, and σF is the electrical conductivity.
The transducer has an inherent shunting capacitance C0, which occasions current loss i0. The attendant preamplifier provides regenerative feedback to neutralize this loss, as shown in FIG. 3.
FIG. 4 shows Hentschel's measurement of triboelectric noise ((7) Hentschel, Rainer, “Über Induktive Durchflussmessung Mischleitender und Isolierender Flüssigkeiten,” Doktor-Ingenieur dissertation, Technical University at Hanover (1973)). The noise is a statistical time series, the voltage continuous in time, and has a spectrum of about f−2.6. When voltage samples are taken Δt apart, the difference ΔV in noise voltage is small if Δt is small; and ΔV approaches zero as Δt approaches zero. However, at any time t the noise voltage may be sizeable. We see the need to take voltage samples a small Δt apart, and form their differences.